Erratum: Self-induced conversion in dense neutrino gases: Pendulum in flavor space [Phys. Rev. D74, 105010 (2006)]

Abstract

Neutrino-neutrino interactions can lead to collective flavour conversion effects in supernovae and in the early universe. We demonstrate that the case of "bipolar" oscillations, where a dense gas of neutrinos and antineutrinos in equal numbers completely converts from one flavour to another even if the mixing angle is small, is equivalent to a pendulum in flavour space. Bipolar flavour conversion corresponds to the swinging of the pendulum, which begins in an unstable upright position (the initial flavour), and passes through momentarily the vertically downward position (the other flavour) in the course of its motion. The time scale to complete one cycle of oscillation depends logarithmically on the vacuum mixing angle. Likewise, the presence of an ordinary medium can be shown analytically to contribute to a logarithmic increase in the bipolar conversion period. We further find that a more complex (and realistic) system of unequal numbers of neutrinos and antineutrinos is analogous to a spinning top subject to a torque. This analogy easily explains how such a system can oscillate in both the bipolar and the synchronised mode, depending on the neutrino density and the size of the neutrino-antineutrino asymmetry. Our simple model applies strictly only to isotropic neutrino gasses. In more general cases, and especially for neutrinos streaming from a supernova core, different modes couple to each other with unequal strength, an effect that can lead to kinematical decoherence in flavour space rather than collective oscillations. The exact circumstances under which collective oscillations occur in non-isotropic media remain to be understood.

Resonances driven by a neutrino gyroscope and collective neutrino oscillations in supernovae

“…As discussed in [16,17] and repeated below, the system governed by the above equations is mathematically equivalent to a gyroscope in a uniform gravitational field.…”

Decoherence in supernova neutrino transformations suppressed by deleptonization

“…In the previous literature it was recognized that a constant matter profile essentially reduces the effective mixing angle so that matter should have the same influence as a small vacuum mixing angle [4,7]. We illustrate this point in Fig.…”

“…× Lν This is significantly larger than the assumptions of previous studies [5,7]. Unless otherwise stated, we always use the benchmark values for the different parameters summarized in Table I.…”

“…A distribution of energies does not lead to kinematical decoherence in the context of collective neutrino oscillations [7] so that the number of energy bins is not a crucial parameter. Of course, to resolve the energy-dependent behavior and especially the spectral splits [5,9,10,11], a sufficiently fine-grained binning is required.…”

“…Therefore, the main impact of a modified µ is to change r synch and thus to push the collective pair conversions to larger radii. The oscillations are synchronized if [7] µ ω >…”